The so called Wilkinson’s Schur complement trick plays a prominent role in the theory of eigenvalue estimates for finite matrices. We apply this technique to the problem of obtaining Ritz value spectral estimates for a positive definite self-adjoint operator in a Hilbert space. New estimates have a form of a Temple–Kato like inequality and are particularly suited to a situation in which we are ...

the main result of this article is that for collections of entry-wise non-negative matrices the property of possessing a standard triangularization is stable under approximation. the methodology introduced to prove this result allows us to offer quick proofs of the corresponding results of [b. r. yahaghi, near triangularizability implies triangularizability, canad. math. bull. 47, (2004), no. 2...

For A ? L(X), B L(Y) and C L(Y,X) we denote by MC the operator matrix defined on X Y = (A 0 B). In this paper, prove that ?qF(A) ?qF(B) [ C?L(Y,X) ?qF(MC) ?p(B) ?p(A?), where ?qF(.) (resp. ?p(.)) denotes quasi-Fredholm spectrum point spectrum). Furthermore, consider some sufficient conditions for to be have ?qF(MC).

The completely positive operators, which can be viewed as a generalization of the nonnegative matrices, are maps between spaces of linear operators arising in the study of C*-algebras. The existence of the operator analogues of doubly stochastic scalings of matrices is equivalent to a multitude of problems in computer science and mathematics, such rational identity testing in non-commuting vari...